Method for determining pump flow without the use of traditional sensors

ABSTRACT

A technique for determining pump flow without using traditional sensors features steps and modules for creating a calibrated power curve at closed valve conditions at several speeds; calculating coefficients from a normalized power curve based on a pump&#39;s power ratio; and solving a polynomial power equation for flow at the current operating point. The calibrated power curve may be created by increasing the speed of the pump from a minimum speed to a maximum speed and operating the pump with a closed discharge valve. This data is used to correct published performance for shutoff power and best efficiency point power at rated speed in order to determine the pump&#39;s power ratio. It is also used to accurately determine closed valve power at the current operating speed. The pump&#39;s power ratio is determined by the equation: P ratio =P shutoff @100% /P BEP     —     corr . The polynomial power equation may, for example, include a 3rd order polynomial equation developed using coefficients from the normalized power versus flow curve, and corrections may be made for speed, hydraulic efficiency and specific gravity in the polynomial power equation. Complex roots may be determined to solve the 3rd order polynomial equation using either Muller&#39;s method or some other suitable method, and the calculated actual flow may be determined for a specific operating point.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application claims benefit to provisional patent applicationSer. No. 60/780,546, filed 8 Mar. 2006, entitled “Method for DeterminingPump Flow Without the Use of Traditional Sensors,” (911-2.24-1/05GI003),and is also related to patent application Ser. No. 11/601,373, filed 17Nov. 2006, entitled “Method and Apparatus For Pump Protection Withoutthe Use of Traditional Sensors,” (911-2.22-1/05GI002), and is alsorelated to provisional patent application Ser. No. 60/780,547, filed 8Mar. 2006, entitled “Method for Optimizing Valve Position and Pump Speedin a PID Control Valve System without the Use of External Sensors”(911-2.23-1/06GI001). All of these patent applications are incorporatedherein by reference in their entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a pump system having a pump, includinga centrifugal pump; and more particularly to a method for determiningpump flow without the use of traditional sensors.

2. Brief Description of Related Art

Pumping devices known in the art, techniques associated with the same,and their shortcomings are as follows:

Controllers for pumps are known to use the Pump Affinity Laws, which areapproximations of how the performance (flow, head, power) of acentrifugal pump is affected by speed and by impeller trim. While theaffinity laws are effective for general estimations, the factoringcoefficient for power frequently results in an over or under estimationof power based upon the operating speed, size and specific speed of thepump. This inaccuracy directly influences algorithms for pump protectionand flow prediction that can be found in Programmable Logic Controllers(PLC), Distributed Control Systems (DCS), and Variable Frequency Drives(VFD).

Furthermore, when creating pump performance maps, variations in actualpump performance from standard performance curves significantly degradesthe accuracy of flow and/or pump condition estimation. The most commonsolution to this is to perform a pump performance test at multiplespeeds to confirm accurate pump performance. However, this solution canbecome timely, application specific and quite costly. In view of this,there is a need in the industry for a technique that overcomes the errorof the affinity laws.

U.S. Pat. No. 6,715,996 B2, issued to Moeller, discloses a method forthe operation of a centrifugal pump that samples the pump power atclosed valve condition for two speeds, determines parasitic losses andcalculates an adjusted power at other frequencies to determine if thepump is operating at closed valve condition. However, methods to correctpower at closed valve condition like this begin to lose accuracy atspeeds below 50% of nominal motor speed and can limit application range.The method of interpolation between power values at other speeds isbased partly on the affinity laws and as such is less accurate.

PCT WO 2005/064167 A1 issued to Witzel, Rolf et al., discloses atechnique that uses a calibrated power/differential pressure curve vsflow vs speed. The calibrated data is stored and compared to currentvalues in order to determine pump flow. This technique requires adifferential pressure transmitter and requires that calibration curvesfor power/Δ pressure vs. flow be stored in the evaluation device. Thismethod is application specific to obtain flow thereby reducingflexibility during field setup. It is also not easily adjusted tocompensate for wear.

U.S. Pat. No. 6,591,697, issued to Henyan, discloses a method fordetermining pump flow rates using motor torque measurements, whichexplains the relationship of torque and speed versus pump flow rate andthe ability to regulate pump flow using a Variable Frequency Drive (VFD)to adjust centrifugal pump speed. However, this technique utilizescalibrated flow vs torque curves for several speeds which areapplication specific thereby reducing flexibility during field setup. Itis also not easily adjusted to compensate for wear.

U.S. Pat. No. 6,464,464 B2, issued to Sabini, et al., discloses anapparatus and method for controlling a pump system based on a controland pump protection algorithm which uses a VFD to regulate flow,pressure or speed of a centrifugal pump. However, this techniquerequires the use of auxiliary instrumentation which adds cost andcomplexity to the drive system, a potential failure point, andunnecessary cost. It also utilizes calibrated Flow vs TDH curves atseveral speeds which are application specific thereby reducingflexibility during field setup.

Furthermore, the following patents were developed in a patentabilitysearch conducted in relation to the present invention. Below is a briefsummary thereof:

U.S. Pat. No. 4,358,821 discloses a method and apparatus for theincorporation of varying flow in the control of process quantities,where the passing flow is measured and the amount of material flowedthrough the process is determined by integration of the results of themeasurement.

U.S. Pat. No. 5,213,477 discloses an apparatus for pump delivery flowrate control, where maximum allowable flow is determined based on arelationship between the available and required net positive suctionhead (NPSH).

U.S. Pat. No. 6,424,873 discloses a method and system for limitingintegral calculation components in a PID controller, based on atechnique where an integral calculation component of a primary PIDcontroller is excluded or a portion thereof or is included in a PIDcalculation.

U.S. Pat. No. 6,546,295 discloses a method of tuning a process controlloop in an industrial process, where field device and processcontrollers are fine-tuned by determining control parameters for thecontrollers that interact to provide a desired process variability.

U.S. Pat. No. 6,554,198 discloses a slope predictive control and digitalPID control for controlling a variable air volume (VAV) box in apressure independent VAV temperature control system, based on atechnique involving a calculation of an error between an airflowsetpoint and measured airflow.

Patent Publication No. 2004/0267395 discloses a system and method fordynamic multi-objective optimization of machine selection, integrationand utilization, based on a technique where asset utilization in anindustrial automation system is modified based on a function of analyzeddiagnostic and machine data.

Patent Publication No. 2005/0237021 discloses a rotatingly drivingdevice of construction machinery, in the form of a method and apparatusfor pumping a fluid at a constant average flow rate.

None of the aforementioned patents or publications teach or suggest thetechnique described herein for determining pump flow without traditionalsensors.

SUMMARY OF THE INVENTION

The present invention provides a new and unique method for determiningpump flow in a centrifugal pump, centrifugal mixer, centrifugal bloweror centrifugal compressor without using traditional sensors, featuringsteps of creating a calibrated power curve at closed valve conditions atseveral speeds; calculating coefficients from a power vs flow curvebased on a pump's power ratio; and solving a power equation for flow atthe current operating point.

The calibrated power curve may be created by increasing the speed of thepump from a minimum speed to a maximum speed while operating the pumpagainst a closed discharge valve and collecting speed and power data atseveral speeds. This data is used to correct published performance forshutoff power and best efficiency point power at rated speed in order todetermine the pump's power ratio. It is also used to accuratelydetermine closed valve power at the current operating speed. This isnecessary because published performance data often differs from actualdata due to seal losses, wear, casting variations etc.

The pump's power ratio is calculated by the equation:

P _(ratio) =P _(shutoff @100%) /P _(BEP) _(—) _(corr).

The power equation may, for example, include a 3rd order polynomialequation developed using coefficients from a normalized power versusflow curve, and corrections may be made for speed and hydraulicefficiency in the polynomial power equation. In addition, complex rootsmay be determined to solve the 3rd order polynomial equation usingeither Muller's method or some other suitable method, and the calculatedactual flow may be determined for a specific operating point.

The steps of the method may be performed on a variable frequency drive(VFD) having one or more modules that implements the features set forthherein, as well as a programmable logic controller (PLC).

The present invention may also include a controller having one or moremodules configured for implementing the features set forth herein, aswell as a pump system having such a controller.

BRIEF DESCRIPTION OF THE DRAWING

The drawing includes the following Figures:

FIG. 1 is a block diagram of a basic pump system according to thepresent invention.

FIG. 2 is a flowchart of basic steps performed according to the presentinvention by the controller shown in FIG. 1.

FIG. 3 is a block diagram of a controller shown in FIG. 1 for performingthe basic steps shown in FIG. 2.

FIG. 4 is a graph of curves of % error (HP) versus speed (RPM) usingvarious methods such as cubic interpolation, method X and affinity laws.

FIG. 5 is a graph of curves for power (HP) versus speed (RPM) @ closedvalve condition for actual drive power, tuned power, and affinitymethods.

FIG. 6 is a graph of curves for power (BHP) versus flow (GPM) for actualdrive power, pricebook (w/seal) published data and tuned power correcteddata with polynomial curve fits also shown for each data set.

FIG. 7 is a graph of normalized curves for % power (HP) versus % flow(RPM) at 1700, 2200, 2800, 3570 RPMs actual and as calculated.

FIG. 8 is a graph of curves for tuned power (BHP) versus flow (GPM) foractual flow and calculated flow.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows the basic pump system generally indicated as 2 according tothe present invention, having a controller 4, a motor 6 and a pump 8. Inoperation, and according to the present invention, the controller 4provides for determining pump flow without using traditional sensorsbased on a technique of creating a calibrated power curve at closedvalve conditions at several speeds; calculating coefficients from apower vs flow curve based on a pump's power ratio; and solving a powerequation for flow at the current operating point, consistent with thatshown and described herein.

FIG. 2 shows, by way of example, a flowchart generally indicated as 10having the basic steps 10 a, 10 b, 10 c of the pump flow determinationalgorithm that may be implemented by the controller 4 according to thepresent invention. The determined flow value may also be used as aninput to a PID control loop to control flow without an externalflowmeter or traditional instrumentation. The flow determinationalgorithm may be embedded in a Variable Frequency Drive or ProgrammableLogic Controller like that shown above in relation to the controller 4in FIG. 1.

According to the present invention, the calibrated power curve may becreated by increasing the speed of the pump from a minimum speed to amaximum speed and operating the pump against a closed discharge valve.This data is used to correct published performance for shutoff power andbest efficiency point power at rated speed in order to determine thepump's power ratio. It is also used to accurately determine closed valvepower at the current operating speed.

The pump's power ratio may be calculated by the equation:

P _(ratio) =P _(shutoff @100%) /P _(BEP) _(—) _(corr).

The power equation may, for example, include a 3rd order polynomialequation developed using coefficients from a normalized power versusflow curve, and corrections may be made for speed and hydraulicefficiency in the polynomial power equation. In addition, complex rootsmay be determined to solve the 3rd order polynomial equation usingeither Muller's method or some other suitable method, and the calculatedactual flow may be determined for a specific operating point.

One advantage of the present invention is that it overcomes the error ofthe affinity laws by sampling power at various speeds at closed valvecondition so that an accurate power curve can be generated at shut-offcondition. By using a proprietary cubic interpolation method the pumppower at closed valve condition can then be determined accurately over awide speed range. See the graphs shown in FIGS. 4 and 5.

Power obtained using published pump performance curve data often differsfrom the actual power due to pump seal losses which vary linearly. Thedifference between actual and published power at shutoff condition canbe used to offset (adjust) the published curve power at the pump's bestefficiency point (BEP) since seal losses are constant for a given speed.This approach eliminates the need for a highly accurate pump performancecurve (e.g. factory test) or a more complicated field calibrationprocess. This process creates a more accurate estimation of P_(BEP) andP_(SO) at various speeds. This data can then be used for more advancedmodeling of pump performance based upon minimal external data.

The method of integrating the normalized power coefficients into a3^(rd) order power equation eliminates the need to perform flowcalibrations against parameters such as torque, power or pressure atvarious speeds, eliminates the need for external transmitters andprovides application flexibility during field setup. The presentinvention can provide for wear compensation by periodically performingthe tuning described in step A below.

FIG. 3: The Controller 4

FIG. 3 shows the basic modules 4 a, 4 b, 4 c, 4 d of the controller 4.Many different types and kind of controllers and control modules forcontrolling pumps are known in the art. Based on an understanding ofsuch known controllers and control modules, a person skilled in the artwould be able to implement control modules such as 4 a, 4 b, 4 c andconfigure the same to perform functionality consistent with thatdescribed herein, including creating a calibrated power curve at closedvalve conditions at several speeds; calculating a normalized power curvecoefficient based on a pump's power ratio; and solving a polynomialpower equation for flow at the current operating point, such as thatshown in FIG. 2 and described above, in accordance with the presentinvention. By way of example, the functionality of the modules 4 a, 4 b,4 c may be implemented using hardware, software, firmware, or acombination thereof, although the scope of the invention is not intendedto be limited to any particular embodiment thereof. In a typicalsoftware implementation, such a module would be one or moremicroprocessor-based architectures having a microprocessor, a randomaccess memory (RAM), a read only memory (ROM), input/output devices andcontrol, data and address buses connecting the same. A person skilled inthe art would be able to program such a microprocessor-basedimplementation to perform the functionality described herein withoutundue experimentation. The scope of the invention is not intended to belimited to any particular implementation using technology known or laterdeveloped in the future.

The controller has other controller modules 4 d that are known in theart, that do not form part of the underlying invention, and that are notdescribed in detail herein.

The Motor 6 and Pump 8

The motor 6 and pump 8 are known in the art and not described in detailherein. Moreover, the scope of the invention is not intended to belimited to any particular type or kind thereof that is either now knownor later developed in the future. Moreover still, the scope of theinvention is also intended to include using the technique according tothe present invention in relation to controlling the operation of acentrifugal pump, centrifugal mixer, centrifugal blower or centrifugalcompressor.

The Implementation

This method of flow calculation has two basic steps:

Step A is to create a calibrated power curve at closed valve conditionat several speeds.

Step B is to calculate the normalized power curve coefficients based ona pump's power ratio and solve a 3^(rd) order polynomial power equationfor flow at the current operating point.

Step A

The logic according to the present invention works by increasing pumpspeed from a predetermined minimum speed (e.g. 30% of maximum speed) toa higher level of speed (e.g. 60% maximum speed) while the pump isoperating with a closed discharge valve. The ratio of speeds should beabout 2:1. Power is then measured at these speeds and at 100% maximumspeed and corrected for a specific gravity=1.

The shutoff power at any speed can then be determined by a proprietarycubic interpolation method:

The coefficients A-F are calculated as follows:

A=(P _(SO) _(—) _(30%))/(N _(30%))

B=(P _(SO) _(—) _(60%) −P _(SO) _(—) _(30%))/(N _(60%) −N _(30%))

C=(B−A)/(N _(60%) −N _(30%))

D=(P _(SO) _(—) _(100%) −P _(SO) _(—) _(60%))/(N _(100%) −N _(60%))

E=(D−B)/((N _(100%) −N _(30%))

F=(E−C)/(N _(100%))

The shutoff power at any speed is calculated as follows:

P _(SO) _(—) _(N %) =A(N _(ACT))+C(N _(ACT))(N _(ACT) −N _(30%))+F(N_(ACT))(N _(ACT) −N _(30%))(N _(ACT) −N _(60%)),

Where: P_(SO) _(—) ₃₀%=P_(Meas) _(—) _(30%)/SG is the measured shutoffPower at 30% motor nominal speed corrected to a Specific Gravity=1,P_(SO) _(—) _(60%)=P_(Meas) _(—) _(60%)/SG is the measured shutoff Powerat 60% motor nominal speed corrected to a Specific Gravity=1, and P_(SO)_(—) _(100%)=P_(Meas) _(—) _(100%)/SG is the measured shutoff Power at100% motor nominal speed corrected to a Specific Gravity=1.

It is noted that for some embodiments, such as for sealless pumps, eddycurrent loss estimations must be removed from measured closed powervalues.

It is also noted that to improve accuracy for some embodiments, such assmall hp pumps applied on liquids with specific gravity other than 1.0,mechanical losses (such as seals and bearings) can be compensated for inthe above shutoff power equations as follows:

P _(SO) _(—) _(N)=[(P _(Meas) _(—) _(N %)−(Mech Loss×N _(Act) /N_(Rated)))/SG]+(Mech Loss×N _(Act) /N _(Rated)),

where

SG=specific Gravity, N_(30%)=Speed at 30% motor nominal speed,N_(60%)=Speed at 60% motor nominal speed, and N_(100%)=Speed at 100%motor nominal speed.

FIG. 5 is a graph that shows how the tuned power vs speed curve comparesto the affinity law power correction at closed valve (shutoff) conditionvs actual power.

In higher power pumps, it is necessary to limit speed during tuning inorder to prevent the pump from overheating. In this case the power at100% speed can be calculated from:

P _(SO) _(—) _(100%)=(N _(100%) /N _(60%))^(KSO) ×P _(SO) _(—) _(60%),

where KSO is a shutoff exponent with a typical value of 3.0.

The final step of the logic according to the present invention is toestimate the Power at the Best Efficiency Point (BEP). This functionrelies upon the observation that while the actual values of P_(BEP) andP_(SO) on any given pump may vary greatly from the published performancecurve, the slope of the power curve remains relatively constant.

P _(BEP corr)=(P _(SO) _(100%) −P _(SO))+P _(BEP),

Where:

P_(SO)=Pump power at shutoff at 100% speed from published curve, and

P_(BEP)=Pump power at BEP at 100% speed from published curve.

FIG. 6 is a graph that shows how the tuned power vs flow curve relatesto the published pricebook curve. Note the slope of both curves are thesame.

Other less accurate approximations can also be made to obtain afactoring coefficient “K_(SO)” which can be estimated by taking theratio of the natural log of the power ratio to the speed ratio, asfollows:

KSO=LN(P _(so1) /P _(so2))/LN(N ₁ /N ₂),

Where:

P_(so1)=measured shutoff power at speed N₁, and

P_(so2)=measured shutoff power at speed N₂.

The shutoff power at any speed can then be determined by:

P _(SO xrpm) =P _(SO yrpm) ×(N _(xrpm) /N _(yrpm))^(KSO),

Where:

P_(SO xrpm)=shutoff power at speed N_(xrpm), and

P_(SO yrpm)=shutoff power at speed N_(yrpm).

Step B

In order to determine a calculated flow value normalized power curvesare calculated based on the Pump's Power Ratio,

where:

P _(Ratio) =P _(SO) _(—) _(100%) /P _(BEP corr).

The normalization curves are particular to a pump's Power Ratio andspecific speed. Specific speed is a numerical value which relates to thehydraulic performance of a centrifugal pump.

FIG. 7 is a graph that shows, by way of example, normalization curvesplotted for several speeds for a 2×3-13 end suction pump having aP_(Ratio)=0.45 and a specific speed of 836.

The table below shows actual vs. normalized test data for flow and powerfor the 2×3-13 pump at 3570 rpm.

Normalized Normalized Flow, Gpm Flow Power, HP Power  0 0.00  79.8 0.45188 0.24 102.7 0.58 398 0.51 129.2 0.73 590 0.76 154.5 0.87 775 Bep 1.00177.2 Bep 1.00 Flow HP 960 1.24 198.7 1.12

A 3^(rd) order polynomial power equation was developed using thecoefficients from the normalized power vs flow curve. Corrections aremade for speed and hydraulic efficiency in the power equation.

Normalized power vs flow curve coefficients a, b and c define thenormalized curve shape, as follows:

0=[(P _(BEP CORR)(a))/((Q _(BEP))³(η_(HBEP) _(—) _(CORR)))](Q_(Act))³+[((N _(Act))(P _(BEPCORR))(b))/((N _(Rated)) (Q_(BEP))²(η_(HBEP) _(—CORR) ))](Q _(Act))²+[((N _(Act))²(P_(BEP CORR))(c))/((N _(Rated))²(Q _(BEP)) (η_(HBEP) _(—) _(CORR)))](Q_(Act))+(P _(SO) _(—) _(N %)−(P _(ACT) /S.G.)),

Where: P_(BEP CORR)=corrected pump power at BEP as determined from thetuned power curve at rated speed, Q_(BEP)=Pump Flow at BEP at ratedspeed, η_(HBEP) _(—) _(CORR)=hydraulic efficiency correction,η_(HBEP)≅1−0.8/Q_(BEP) ^(0.25) published values typically range from0.7-0.95, N_(Act)=actual operating speed, N_(Rated)=rated speed, P_(SO)_(—) _(N %)=Pump shutoff power at actual operating speed (determinedfrom tuned power curve), P_(ACT)=Actual pump power, S.G.=specificgravity, and Q_(Act)=calculated actual flow at current operating speed.

It is noted again that to improve accuracy for some embodiments, such assmall hp pumps applied on liquids with specific gravity other than 1.0,mechanical losses (such as seals and bearings) can be compensated for inthe above power equation by adjusting P_(ACT) as follows:

P _(ACT CORR)=[((P _(ACT)−(Mech Loss×N _(Act) /N _(Rated)))/S.G.)+(MechLoss×N _(Act) /N _(Rated))].

It is also noted again that, for some embodiments such as seallesspumps, eddy current loss estimations must be removed from actual powerreading in the above power equation.

Complex roots are than determined to solve the 3^(rd) order polynomialusing Mullers Method or other equivalent methods. The calculated actualflow is then determined for the specific operating point. FIG. 8 is agraph that shows the calculated power vs flow curve when plotted for the3^(rd) order polynomial power equation compared to actual flow dataobtained by flowmeter readings.

Since pump wear will effect the pump power requirement and thereforereduce flow accuracy the power calculations can be periodicallycompensated for by periodically performing another calibration asoutlined in step A.

Other Possible Applications

Other possible applications include at least the following:

Pump Load Monitors—Pump load monitors rely upon an accurate modeling ofthe pump power curve to identify minimum flow and shut-off conditions.While most load monitors only monitor power at one speed, this logicwould enable more accurate load monitors for variable speed operation.

Sensorless flow calculations—Sensorless flow estimations rely uponaccurate power curves to estimate pump flow. The use of basic affinitylaws may compromise flow accuracy as speed is decreased. This isespecially true on smaller pumps where losses such as seals and bearingsbecome more prominent and do not factor according to the affinity laws.

Pump Protection Algorithms—sensorless flow measurements can give areliable indication of operating conditions: runout conditions (flow toohigh), operation below minimum pump flow (flow too low) or operationagainst a closed discharge valve.

The Scope of the Invention

It should be understood that, unless stated otherwise herein, any of thefeatures, characteristics, alternatives or modifications describedregarding a particular embodiment herein may also be applied, used, orincorporated with any other embodiment described herein. Also, thedrawings herein are not drawn to scale.

Although the invention has been described and illustrated with respectto exemplary embodiments thereof, the foregoing and various otheradditions and omissions may be made therein and thereto withoutdeparting from the spirit and scope of the present invention.

1. A method for determining pump flow in a centrifugal pump, centrifugalmixer, centrifugal blower or centrifugal compressor comprising: creatinga calibrated power curve at closed valve conditions at several speeds;calculating coefficients from a power vs flow curve based on a pump'spower ratio; and solving a power equation for flow at the currentoperating point.
 2. A method according to claim 1, wherein thecalibrated power curve is created by increasing the speed of the pumpfrom a minimum speed to a maximum speed while operating the pump againsta closed discharge valve and collecting speed and power data at severalspeeds.
 3. A method according to claim 2, wherein the closed valve powerdata is corrected to a specific gravity equal to
 1. 4. A methodaccording to claim 2, wherein for small hp pumps applied on liquids withspecific gravity other than 1.0, mechanical losses (such as seals andbearings) can be compensated for in the measured closed valve powerreadings as follows:P _(SO) _(—) _(N)=[(P _(Meas) _(—) _(N %)−(Mech Loss×N _(Act) /N_(Rated)))/SG]+(Mech Loss×N _(Act) /N _(Rated)), where SG=specificGravity.
 5. A method according to claim 2, wherein for sealless pumpseddy current loss estimations must be removed from the actual closedvalve power readings.
 6. A method according to claim 2, wherein forhigher power pumps, to minimize heating of the pumped liquid the shutoffpower at 100% speed can be calculated from the equation:P _(SO) _(—) _(100%)=(N _(100%) /N _(60%))^(KSO) ×P _(SO) _(—) _(60%),where KSO is a shutoff exponent with a typical value of 3.0.
 7. A methodaccording to claim 2, wherein the closed valve power at any speed can beaccurately determined by the following cubic interpolation method:A=(PSO _(—)30%)/(N30%),B=(P _(SO) _(—) _(60%) −P _(SO) _(—) _(30%))/(N _(60%) −N _(30%)),C=(B−A)/(N _(60%) −N _(30%)),D=(P _(SO) _(—) _(100%) −P _(SO) _(—) _(60%))/(N _(100%) −N _(60%)),E=(D−B)/((N _(100%) −N _(30%)), andF=(E−C)/(N _(100%)); and wherein the shutoff power at any speed iscalculated as follows:P _(SO) _(—) _(N %) =A(N _(ACT))+C(N _(ACT))(N _(ACT) −N _(30%))+F(N_(ACT))(N _(ACT) −N _(30%))(N _(ACT) −N _(60%)), where: P_(SO) _(—)_(30%)=P_(Meas) _(—) _(30%)/SG is the measured shutoff Power at 30%motor nominal speed corrected to a Specific Gravity=1, P_(SO) _(—)_(60%)=P_(Meas) _(—) _(60%)/SG is the measured shutoff Power at 60%motor nominal speed corrected to a Specific Gravity=1, and P_(SO) _(—)_(100%)=P_(Meas) _(—) _(100%)/SG is the measured shutoff Power at 100%motor nominal speed corrected to a Specific Gravity=1.
 8. A methodaccording to claim 2, wherein the published power at the best efficiencypoint at rated speed is corrected based on actual closed valve powerdata.
 9. A method according to claim 8, wherein the published power atbest efficiency point is corrected according to the equation:P _(BEP corr)=(P _(SO) _(100%) −P _(SO))+P _(BEP), where: P_(SO)=Pumppower at shutoff at 100% speed from published curve, P_(BEP)=Pump powerat BEP at 100% speed from published curve, and P_(SO) _(100%) =actualclosed valve power at 100% speed.
 10. A method according to claim 1,wherein the pump's power ratio is determined by the equation:P _(ratio) =P _(shutoff @100%) /P _(BEP) _(—) _(corr).
 11. A methodaccording to claim 1, wherein the power equation is a polynomialequation developed using coefficients from the power versus flow curve.12. A method according to claim 11, wherein the polynomial powerequation is:0=[(P _(BEP CORR)(a))/((Q _(BEP))³(η_(HBEP) _(—) _(CORR)))](Q_(Act))³+[((N _(Act))(P _(BEPCORR))(b))/((N _(Rated)) (Q_(BEP))²(η_(HBEP) _(—) _(CORR)))](Q _(Act))²+[((N _(Act))²(P_(BEP CORR))(c))/((N _(Rated))²(Q _(BEP))(η_(HBEP) _(—) _(CORR)))](Q_(Act))+(P _(SO) _(N %) −(P _(ACT) /S.G.)), where:P_(BEP CORR)=corrected pump power at BEP as determined from the tunedpower curve at rated speed, Q_(BEP)=Pump Flow at BEP at rated speed,η_(HBEP) _(—) _(CORR)=hydraulic efficiency correction,η_(HBEP)≅1−0.8/Q_(BEP) ^(0.25) published values typically range from0.7-0.95, N_(Act)=actual operating speed, N_(Rated)=rated speed, P_(SO)_(—) _(N %)=Pump shutoff power at actual operating speed (determinedfrom tuned power curve), P_(ACT)=Actual pump power, S.G.=specificgravity, and Q_(Act)=calculated actual flow at current operating speed.13. A method according to claim 12, wherein accuracy for small hp pumpsapplied on liquids with specific gravity other than 1.0, can becompensated for mechanical losses (such as seals and bearings) in thepolynomial power equation by adjusting P_(ACT) as follows:P _(ACT CORR)=[((P _(ACT)−(Mech Loss×N _(Act) /N _(Rated)))/S.G.)+(MechLoss×N _(Act) /N _(Rated))].
 14. A method according to claim 12, whereinfor sealless pumps eddy current loss estimations are removed from theactual power reading in the polynomial power equation.
 15. A methodaccording to claim 11, wherein corrections are made for speed, hydraulicefficiency and specific gravity in the polynomial power equation.
 16. Amethod according to claim 15, wherein complex roots are determined tosolve the polynomial equation using either Muller's method or some othersuitable method.
 17. A method according to claim 16, wherein thecalculated actual flow is determined for a specific operating point. 18.A method according to claim 1, wherein the steps of the method areperformed on a variable frequency drive (VFD) or a programmable logiccontroller (PLC).
 19. A method according to claim 1, wherein thedetermined flow value may be used as input to a PID controller tocontrol flow without the need for a flowmeter or other externalinstrumentation.
 20. A controller for determining pump flow in acentrifugal pump, centrifugal mixer, centrifugal blower or centrifugalcompressor comprising: a module configured for creating a calibratedpower curve at closed valve conditions at several speeds; a moduleconfigured for calculating coefficients from a power vs flow curve basedon a pump's power ratio; and a module configured for solving a powerequation for flow at the current operating point.
 21. A controlleraccording to claim 20, wherein the calibrated power curve is created byincreasing the speed of the pump from a minimum speed to a maximum speedwhile operating the pump against a closed discharge valve and collectingspeed and power data at several speeds.
 22. A controller according toclaim 21, wherein the closed valve power data is corrected to a specificgravity equal to
 1. 23. A controller according to claim 21, wherein forsmall hp pumps applied on liquids with specific gravity other than 1.0,mechanical losses (such as seals and bearings) can be compensated for inthe measured closed valve power readings as follows:P _(SO) _(—) _(N)=[(P _(Meas) _(—) _(N %)−(Mech Loss×N _(Act) /N_(Rated)))/SG]+(Mech Loss×N _(Act) /N _(Rated)), where SG=specificGravity.
 24. A controller according to claim 21, wherein for seallesspumps eddy current loss estimations are removed from the actual closedvalve power readings.
 25. A controller according to claim 21, whereinfor higher power pumps, to minimize heating of the pumped liquid theshutoff power at 100% speed can be calculated from the equation:P _(SO) _(—100%) =(N _(100%) /N _(60%))^(KSO) ×P _(SO) _(—) _(60%),where KSO is a shutoff exponent with a typical value of 3.0.
 26. Acontroller according to claim 21, wherein the closed valve power at anyspeed can be accurately determined by the following cubic interpolationmethod:A=(P SO _(—)30%)/(N30%),B=(P _(SO) _(—) _(60%) −P _(SO) _(—) _(30%))/(N _(60%) −N _(30%)),C=(B−A)/(N _(60%) −N _(30%)),D=(P _(SO) _(—) _(100%) −P _(SO) _(—) _(60%))/(N _(100%) −N _(60%)),E=(D−B)/((N _(100%) −N _(30%)), andF=(E−C)/(N _(100%)); and wherein the shutoff power at any speed iscalculated as follows:P _(SO) _(—) _(N %) =A(N _(ACT))+C(N _(ACT))+C(N _(ACT) −N _(30%))+F(N_(ACT))(N _(ACT) −N ₃₀%)(N _(ACT) −N _(60%)), where: P_(SO) _(—)₃₀%=P_(Meas) _(—) ₃₀%/SG: measured shutoff Power at 30% motor nominalspeed corrected to a Specific Gravity=1, P_(SO) _(—) _(60%)=P_(Meas)_(—) ₆₀%/SG: measured shutoff Power at 60% motor nominal speed correctedto a Specific Gravity=1, and P_(SO) _(—) _(100%)=P_(Meas) _(—) ₁₀₀/SG:measured shutoff Power at 100% motor nominal speed corrected to aSpecific Gravity=1.
 27. A controller according to claim 21, wherein thepublished power at the best efficiency point at rated speed is correctedbased on actual closed valve power data.
 28. A controller according toclaim 27, wherein the published power at best efficiency point iscorrected according to the equation:P _(BEP corr)=(P _(SO) _(100%) −P _(SO))+P _(BEP), where: P_(SO)=Pumppower at shutoff at 100% speed from published curve, P_(BEP)=Pump powerat BEP at 100% speed from published curve, and P_(SO) _(100%) =actualclosed valve power at 100% speed.
 29. A controller according to claim20, wherein the pump's power ratio is determined by the equation:P _(ratio) =P _(shutoff @100%) /P _(BEP) _(—) _(corr).
 30. A controlleraccording to claim 20, wherein the power equation is a polynomialequation developed using coefficients from the power versus flow curve.31. A controller according to claim 30, wherein the polynomial powerequation is:0=[(P _(BEP CORR)(a))/((Q _(BEP))³(η_(HBEP) _(—) _(CORR)))](Q_(Act))³+[((N _(Act))(P _(BEPCORR)) (b))/((N _(Rated)) (Q_(BEP))²(η_(HBEP) _(—) _(CORR)))](Q _(Act))²+[((N _(Act))²(P_(BEP CORR))(c))/((N _(Rated))²(Q _(BEP))(η_(HBEP) _(—) _(CORR)))](Q_(Act))+(P _(SO) _(—) _(N %)−(P _(ACT) /S.G.)), where:P_(BEP CORR)=corrected pump power at BEP as determined from the tunedpower curve at rated speed, Q_(BEP)=Pump Flow at BEP at rated speed,η_(HBEP) _(—) _(CORR)=hydraulic efficiency correction,η_(HBEP)≅1−0.8/Q_(BEP) ^(0.25) published values typically range from0.7-0.95, N_(Act)=actual operating speed, N_(Rated)=rated speed, P_(SO)_(—) _(N %)=Pump shutoff power at actual operating speed (determinedfrom tuned power curve), P_(ACT)=Actual pump power, S.G.=specificgravity, and Q_(Act)=calculated actual flow at current operating speed.32. A controller according to claim 30, wherein accuracy for small hppumps applied on liquids with specific gravity other than 1.0, can becompensated for mechanical losses (such as seals and bearings) in thepolynomial power equation by adjusting P_(ACT) as follows:P _(ACT CORR)=[((P _(ACT)−(Mech Loss×N _(Act) /N _(Rated)))/S.G.)+(MechLoss×N _(Act) /N _(Rated))].
 33. A controller according to claim 30,wherein for sealless pumps eddy current loss estimations are removedfrom the actual power reading in the polynomial power equation.
 34. Acontroller according to claim 30, wherein corrections are made forspeed, hydraulic efficiency and specific gravity in the polynomial powerequation.
 35. A controller according to claim 34, wherein complex rootsare determined to solve the polynomial equation using either Muller'smethod or some other suitable method.
 36. A controller according toclaim 35, wherein the calculated actual flow is determined for aspecific operating point.
 37. A controller according to claim 20,wherein the controller includes, or forms part of, a variable frequencydrive (VFD) or a programmable logic controller (PLC).
 38. A controlleraccording to claim 20, wherein the determined flow value may be used asinput to a PID controller to control flow without the need for aflowmeter or other external instrumentation.
 39. A system having acontroller for determining pump flow in a centrifugal pump, centrifugalmixer, centrifugal blower or centrifugal compressor, the controllercomprising: a module configured for creating a calibrated power curve atclosed valve conditions at several speeds; a module configured forcalculating coefficients from a power vs flow curve based on a pump'spower ratio; and a module configured for solving a power equation forflow at the current operating point.
 40. A pump system according toclaim 39, wherein the calibrated power curve is created by increasingthe speed of the pump from a minimum speed to a maximum speed whileoperating the pump against a closed discharge valve and collecting speedand power data at several speeds.
 41. A pump system according to claim40, wherein the closed valve power data is corrected to a specificgravity equal to
 1. 42. A pump system according to claim 40, wherein forsmall hp pumps applied on liquids with specific gravity other than 1.0,mechanical losses (such as seals and bearings) can be compensated for inthe measured closed valve power readings as follows:P _(SO) _(—) _(N)=[(P _(Meas) _(—) _(N %)−(Mech Loss×N _(Act) /N_(Rated)))/SG]+(Mech Loss×N _(Act) /N _(Rated)), where SG=specificGravity.
 43. A pump system according to claim 40, wherein for seallesspumps eddy current loss estimations are removed from the actual closedvalve power readings.
 44. A pump system according to claim 40, whereinfor higher power pumps, to minimize heating of the pumped liquid theshutoff power at 100% speed can be calculated from the equation:P _(SO) _(—) _(100%)=(N _(100%) /N _(60%))^(KSO) ×P _(SO) _(—) _(60%),where KSO is a shutoff exponent with a typical value of 3.0.
 45. A pumpsystem according to claim 40, wherein the closed valve power at anyspeed can be accurately determined by the following cubic interpolationmethod:A=(PSO _(—)30%)/(N30%),B=(P _(SO) _(—) _(60%) −P _(SO) _(—) ₃₀%)/(N _(60%) −N _(30%)),C=(B−A)/(N _(60%) −N _(30%)),D=(P _(SO) _(—) _(100%) −P _(SO) _(—) _(60%))/(N _(100%) −N _(60%)),E=(D−B)/((N _(100%) −N _(30%)), andF=(E−C)/(N _(100%)); and wherein the shutoff power at any speed iscalculated as follows:P _(SO) _(—) _(N %) =A(N _(ACT))+C(N _(ACT))(N _(ACT) −N _(30%))+F(N_(ACT))(N _(ACT) −N _(30%))(N _(ACT) −N _(60%)), where: P_(SO) _(—)_(30%)=P_(Meas) _(—) _(30%)/SG: measured shutoff Power at 30% motornominal speed corrected to a Specific Gravity=1, P_(SO) _(—)_(60%)=P_(Meas) _(—) _(60%)/SG: measured shutoff Power at 60% motornominal speed corrected to a Specific Gravity=1, and P_(SO) _(—)_(100%)=P_(Meas) _(—) _(100%)/SG: measured shutoff Power at 100% motornominal speed corrected to a Specific Gravity=1.
 46. A pump systemaccording to claim 40, wherein the published power at the bestefficiency point at rated speed is corrected based on actual closedvalve power data.
 47. A pump system according to claim 46, wherein thepublished power at best efficiency point is corrected according to theequation:P _(BEP corr)=(P _(SO) _(100%) −P _(SO))+P _(BEP), where: P_(SO)=Pumppower at shutoff at 100% speed from published curve, P_(BEP)=Pump powerat BEP at 100% speed from published curve, and P_(SO) _(100%) =actualclosed valve power at 100% speed.
 48. A pump system according to claim39, wherein the pump's power ratio is determined by the equation:P _(ratio) =P _(shutoff @ 100%) /P _(BEP) _(—) _(corr).
 49. A pumpsystem according to claim 39, wherein the power equation is a polynomialequation developed using coefficients from the power versus flow curve.50. A pump system according to claim 49, wherein the polynomial powerequation is:0=[(P _(BEP CORR)(a))/((Q _(BEP))³(η_(HBEP) _(—) _(CORR)))](Q_(Act))³+[((N _(Act))(P _(BEPCORR)) (b))/((N _(Rated)) (Q_(BEP))²(η_(HBEP) _(—) _(CORR)))](Q _(Act))²+[((N _(Act))²(P_(BEP CORR))(c))/((N _(Rated))²(Q _(BEP))(η_(HBEP) _(—) _(CORR)))](Q_(Act))+(P _(SO) _(—) _(N %)−(P _(ACT) /S.G.)), where:P_(BEP CORR)=corrected pump power at BEP as determined from the tunedpower curve at rated speed, Q_(BEP)=Pump Flow at BEP at rated speed,η_(HBEP) _(—) _(CORR)=hydraulic efficiency correction,η_(HBEP)≅1−0.8/Q_(BEP) ^(0.25) published values typically range from0.7-0.95, N_(Act)=actual operating speed, N_(Rated)=rated speed, P_(SO)_(—) _(N %)=Pump shutoff power at actual operating speed (determinedfrom tuned power curve), P_(ACT)=Actual pump power, S.G.=specificgravity, and Q_(Act)=calculated actual flow at current operating speed.51. A pump system according to claim 49, wherein accuracy for small hppumps applied on liquids with specific gravity other than 1.0, can becompensated for mechanical losses (such as seals and bearings) in thepolynomial power equation by adjusting P_(ACT) as follows:P _(ACT CORR)=[((P _(ACT)−(Mech Loss×N _(Act) /N _(Rated)))/S.G.)+(MechLoss×N _(Act) /N _(Rated))].
 52. A pump system according to claim 49,wherein for sealless pumps eddy current loss estimations are removedfrom the actual power reading in the polynomial power equation.
 53. Apump system according to claim 49, wherein corrections are made forspeed, hydraulic efficiency and specific gravity in the polynomial powerequation.
 54. A pump system according to claim 53, wherein complex rootsare determined to solve the polynomial equation using either Muller'smethod or some other suitable method.
 55. A pump system according toclaim 54, wherein the calculated actual flow is determined for aspecific operating point.
 56. A pump system according to claim 39,wherein the controller includes, or forms part of, a variable frequencydrive (VFD) or a programmable logic controller (PLC).
 57. A pump systemaccording to claim 39, wherein the determined flow value may be used asinput to a PID controller to control flow without the need for aflowmeter or other external instrumentation.